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Factoring Ideals in Integral Domains
by Evan Houston Marco Fontana Thomas LucasThis volume provides a wide-ranging survey of, and many new results on, various important types of ideal factorization actively investigated by several authors in recent years. Examples of domains studied include (1) those with weak factorization, in which each nonzero, nondivisorial ideal can be factored as the product of its divisorial closure and a product of maximal ideals and (2) those with pseudo-Dedekind factorization, in which each nonzero, noninvertible ideal can be factored as the product of an invertible ideal with a product of pairwise comaximal prime ideals. Prüfer domains play a central role in our study, but many non-Prüfer examples are considered as well.
Factorization in Integral Domains (Lecture Notes In Pure And Applied Mathematics Ser. #189)
by Daniel AndersonThe contents in this work are taken from both the University of Iowa's Conference on Factorization in Integral Domains, and the 909th Meeting of the American Mathematical Society's Special Session in Commutative Ring Theory held in Iowa City. The text gathers current work on factorization in integral domains and monoids, and the theory of divisibility, emphasizing possible different lengths of factorization into irreducible elements.
Factorization: Unique and Otherwise
by Steven H. WeintraubThe concept of factorization, familiar in the ordinary system of whole numbers that can be written as a unique product of prime numbers, plays a central role in modern mathematics and its applications. This exposition of the classic theory leads the reader to an understanding of the current knowledge of the subject and its connections to other math
Facts and Factors (Mathematics in Context)
by Meike Abels Jan De Lange Margaret A. PliggeThe numbers we use today are widely used by people all over the world. This might surprise you since there are about 190 independent countries in the world, speaking over 5,000 different languages! This was not always the case. In the unit Facts and Factors, you will investigate how ancient civilizations wrote numbers and performed number computations.
Fading and Shadowing in Wireless Systems
by P. Mohana ShankarThe study of signal transmission and deterioration in signal characteristics as the signal propagates through wireless channels is of great significance. The book presents a comprehensive view of channel degradation arising from fading and shadowing. Various statistical models including simple, hybrid, compound, complex and cascaded ones are presented with detailed derivations along with measures to quantify the deterioration such as the amount of fading, error rates and outage probabilities. The models range from the Rayleigh and Rician through Suzuki, generalized K, cascaded and alpha-mu and similar ones. This is followed by the analysis of mitigation of fading and shadowing through diversity (simple, hybrid, micro- and macro- level) and combining algorithms. The density and distribution functions, error rates and outages are derived and results analyzed to quantify the improvements. The effects of co-channel interference before and after the implementation of diversity are also analyzed. To facilitate easy understanding of the models and analysis, the background information in terms of probability and random variables is presented with relevant derivations of densities of linear and nonlinear transformation of random variables, the sums, products, ratios as well as order statistics of random variables of all types. The book also provides material on digital modems of interest in wireless systems. Thus, the book with 1100+ equations and 350+ Matlab generated figures and tables is an ideal source for students, educators, researchers and professionals in wireless communications allowing access to information currently unavailable.
Fair Queueing
by Youngsub ChunThis monograph provides a detailed analysis on fair queueing rules from a normative, a strategic, and a non-cooperative viewpoint. The queueing problem is concerned with the following situation: There is a group of agents who must be served in a facility. The facility can handle only one agent at a time and agents incur waiting costs. The problem is to find the order in which to serve agents and monetary transfers they should receive. The queueing problem has been studied extensively in the recent literature.
Fair Share: 111 Problems from Ahmes to Aumann
by Isaac ElishakoffKofi Annan, former Secretary General of the United Nations, argued that “We need to create a world that is equitable, that is stable and a world where we bear in mind the needs of others, and not only what we need immediately. We are all in the same boat.”American businessman, John Landgraf stated: “I hope that most of us believe that we actually would all benefit from living in a more equitable society. If that's not happening, we're squandering human potential.” For the world to be fair, one needs to know how to divide. Without the mathematics of division, humankind cannot function…Marie Antoinette, Queen of France (infamously) said “If people have no bread, let them eat cake,” and while Ahmes ― the scribe of the Rhind Mathematical Papyrus ― dealt with loaves of bread, prosperous people in the twentieth century dealt with cake division, although bread is also uniformly available. You’ll be surprised, but there are at least four books and over 200 scientific (not gastronomical!) papers on cake division. Those authors were not overly concerned with obesity, one can guess, but whether distributing loaves, cakes, chores, or dividends, one needs to master division.This book deals with a wide spectrum of division problems, and provides the historical background, giving a sense of how pervasive division is in our lives. In particular, the second part focuses on a problem that remained open until 1985, when Professor Robert John Aumann (Nobel laureate in Economics, 2005) and Professor Michael Maschler solved it using game-theoretic techniques. Simple alternative solutions are given, which are suitable for high schools and other educational institutions.
Fakt oder Fake? Wie Ihnen Statistik bei der Unterscheidung helfen kann
by Werner G. Müller Andreas Quatember„Alternative Wahrheiten“ beeinträchtigen jeden faktenbasierten Diskurs – egal ob im Fernsehen, in Zeitungen oder in den sozialen Medien. Oft werden dafür datengestützte (Schein-)Argumente vorgebracht und es stellt sich ganz automatisch die Frage nach der Qualität dieser Informationen. Dieses Buch zeigt anhand vieler Beispiele, wie Sie mit einer grundlegenden Statistical Literacy sowohl bewusste statistische Fälschungen als auch unbewusste Irrtümer aufdecken können. Denn beides hat denselben Effekt: Sie werden fehlinformiert, wo Sie sich informiert glauben. Begleiten Sie die Autoren auf einem Ausflug in die spannende Welt der Daten und trainieren Sie Ihre statistischen Kompetenzen im kritischen Umgang mit diesen: Hinterfragen Sie Statistiken, bewerten Sie deren Qualität, lernen Sie das korrekte Interpretieren und faktengerechte Argumentieren mit Daten. Die zu beschreitenden Pfade sind gut beschildert; die Autoren demonstrieren eindrücklich, dass sich eine Basismethodenkompetenz auch mit überschaubaren Mathematikkenntnissen erreichen lässt. Die abwechslungsreichen Themen und Darstellungen bieten auch Anregungen für weitere eigene Exkursionen.
Falling Liquid Films
by C. Ruyer-Quil M. G. Velarde B. Scheid S. KalliadasisFalling Liquid Films gives a detailed review of state-of-the-art theoretical, analytical and numerical methodologies, for the analysis of dissipative wave dynamics and pattern formation on the surface of a film falling down a planar inclined substrate. This prototype is an open-flow hydrodynamic instability, that represents an excellent paradigm for the study of complexity in active nonlinear media with energy supply, dissipation and dispersion. It will also be of use for a more general understanding of specific events characterizing the transition to spatio-temporal chaos and weak/dissipative turbulence. Particular emphasis is given to low-dimensional approximations for such flows through a hierarchy of modeling approaches, including equations of the boundary-layer type, averaged formulations based on weighted residuals approaches and long-wave expansions. Whenever possible the link between theory and experiment is illustrated, and, as a further bridge between the two, the development of order-of-magnitude estimates and scaling arguments is used to facilitate the understanding of basic, underlying physics. This monograph will appeal to advanced graduate students in applied mathematics, science or engineering undertaking research on interfacial fluid mechanics or studying fluid mechanics as part of their program. It will also be of use to researchers working on both applied, fundamental theoretical and experimental aspects of thin film flows, as well as engineers and technologists dealing with processes involving isothermal or heated films. This monograph is largely self-contained and no background on interfacial fluid mechanics is assumed.
Fallzahlberechnung in der medizinischen Forschung: Eine Einführung für Mediziner und Biostatistiker (essentials)
by Meinhard KieserMeinhard Kieser vermittelt anhand realer Beispiele die grundlegenden Prinzipien der Fallzahlberechnung und demonstriert deren Anwendung. F#65533;r die h#65533;ufigsten Anwendungssituationen werden die entsprechenden Fallzahlberechnungsformeln hergeleitet. Einsteiger haben somit die M#65533;glichkeit, die Grundlagen der Fallzahlplanung zu erlernen und einzu#65533;ben. Es werden au#65533;erdem die statistischen Hintergr#65533;nde der Formeln und allgemeinere Zusammenh#65533;nge erl#65533;utert und Hinweise gegeben, was bei jeder Fallzahlberechnung beachtet werden sollte. Damit geht das essential deutlich #65533;ber eine reine Formelsammlung hinaus und ist eine wertvolle Erg#65533;nzung f#65533;r Personen, die bereits in der medizinischen Forschung t#65533;tig sind und Erfahrung bei der Fallzahlberechnung gesammelt haben.
False Feedback in Economics: The Case for Replication (Routledge Studies in Economic Theory, Method and Philosophy)
by Andrin SpeschaThis book investigates why economics makes less visible progress over time than scientific fields with a strong practical component, where interactions with physical technologies play a key role. The thesis of the book is that the main impediment to progress in economics is "false feedback", which it defines as the false result of an empirical study, such as empirical evidence produced by a statistical model that violates some of its assumptions. In contrast to scientific fields that work with physical technologies, false feedback is hard to recognize in economics. Economists thus have difficulties knowing where they stand in their inquiries, and false feedback will regularly lead them in the wrong directions. The book searches for the reasons behind the emergence of false feedback. It thereby contributes to a wider discussion in the field of metascience about the practices of researchers when pursuing their daily business. The book thus offers a case study of metascience for the field of empirical economics. The main strength of the book are the numerous smaller insights it provides throughout. The book delves into deep discussions of various theoretical issues, which it illustrates by many applied examples and a wide array of references, especially to philosophy of science. The book puts flesh on complicated and often abstract subjects, particularly when it comes to controversial topics such as p-hacking. The reader gains an understanding of the main challenges present in empirical economic research and also the possible solutions. The main audience of the book are all applied researchers working with data and, in particular, those who have found certain aspects of their research practice problematic.
Familia: Migration and Adaptation in Baja and Alta California, 1880-1975
by Robert R. Alvarez Jr.Anthropologists, historians, and sociologists will find here a striking challenge to accepted explanations of the northward movement of migrants from Mexico into the United States. Alvarez investigates the life histories of pioneer migrants and their offspring, finding a human dimension to migration which centers on the family. Spanish, American, and English exploits paved the way for exchange between Baja and Alta California. Alvarez shows how cultural stability actually increased as migrants settled in new locations, bringing their common values and memories with them.
Families in Global Perspective
by Jaipaul L. RoopnarineHistorians and anthropologists teach that throughout recorded history and in all present-day societies, families have formed the basic cells of the social fabric of society. No other institution, it seems, is similarly adapted to fulfill the combined economic, emotional, and sexual needs of adults while simultaneously responding to the fundamental requirements of infants, children, and adolescents for sustenance, nurturance, and guidance. At the same time, a wealth of family forms that, additionally, are rapidly changing in the face of worldwide economic and technological transformations, has evolved within societies. It is the purpose of this book to document and explain family life in all its varieties from a global and dynamic point of view.
Families of Automorphic Forms and the Trace Formula
by Werner Müller Sug Woo Shin Nicolas TemplierFeaturing the work of twenty-three internationally-recognized experts, this volume explores the trace formula, spectra of locally symmetric spaces, p-adic families, and other recent techniques from harmonic analysis and representation theory. Each peer-reviewed submission in this volume, based on the Simons Foundation symposium on families of automorphic forms and the trace formula held in Puerto Rico in January-February 2014, is the product of intensive research collaboration by the participants over the course of the seven-day workshop. The goal of each session in the symposium was to bring together researchers with diverse specialties in order to identify key difficulties as well as fruitful approaches being explored in the field. The respective themes were counting cohomological forms, p-adic trace formulas, Hecke fields, slopes of modular forms, and orbital integrals.
Family Demography and Post-2015 Development Agenda in Africa
by Clifford O. OdimegwuThis book is a comprehensive analysis of the structure, determinants and consequences of changes in sub-Saharan African families, thereby representing an Afrocentric description of the emerging trends. It documents various themes in the sub-disciplines of family demography. The first section of the book focuses on philosophical understanding of African family, its theoretical perspectives, and comparative analysis of family in the 20th and 21st centuries. The second section covers family formation, union dissolution, emerging trend in single parenthood, and adolescents in the family. The following section describes types, determinants and consequences of African family changes: health, childbearing, youth development, teen pregnancy and family violence and the last chapter provides systematic evidence on existing laws and policies governing African family structure and dynamics. As such it illustrates the importance of family demography in African demographic discourse and will be an interesting read to scholars and students in the field of demography, social workers, policy makers, departments of Social Development in countries in Africa and relevant international agencies and all those interested in understanding the African family trajectory.
Family Issues on Marriage, Divorce, and Older Adults in Japan
by Fumie KumagaiThis book provides insightful sociological analyses of Japanese demography and families, paying attention not only to national average data, but also to regional variations and community level analyses. In analyzing Japanese family issues such as demographic changes, courtship and marriage, international marriage, divorce, late-life divorce, and the elderly living alone, this book emphasizes the significance of two theoretical frameworks: the dual structure and regional variations of the community network in Japan. By emphasizing the extensive cultural diversity from one region to another, this book represents a paradigm shift from former studies of Japanese families, which relied mostly on national average data. The method of analysis adopted in the study is qualitative, with a historical perspective. The book is thus an invitation to more in-depth, qualitative dialogue in the field of family sociology in Japan. This book will be of great interest not only to Asian scholars, but also to other specialists in comparative family studies around the world.
Family Math Night 6-8: Common Core State Standards in Action
by Jennifer Taylor-Cox Christine OberdorfHost Family Math Nights at your middle school—starting today! Family Math Nights are a great way for teachers to get parents involved in their children’s education and to promote math learning outside of the classroom. In this practical book, you’ll find step-by-step guidelines and activities to help you bring Family Math Nights to life. The enhanced second edition is aligned with the Common Core State Standards for Mathematical Content and Practice with new activities to help students explain their answers and write about math. It also comes with ready-to-use handouts that you can distribute during your event. With the resources in this book, you’ll have everything you need to help students learn essential math concepts—including ratios and proportional relationships, the number system, expressions and equations, geometry, and statistics and probability—in a fun and supportive environment. Special Features: The book is organized by math content, so you can quickly find activities that meet your needs. Each activity is easy to implement and includes a page of instructions educators can use to prepare the station, as well as a page for families that explains the activity and can be photocopied and displayed at the station. All of the family activities can be photocopied or downloaded from our website, www.routledge.com/9781138200999, so that you can distribute them during your event.
Family Ties and Psychosocial Processes in an Ageing Society: Comparative Perspectives (International Perspectives on Aging #42)
by Alejandro KleinThis book contributes to the discussion on the ageing society by addressing the new psycho-social structures of the ageing society, the problems around family bonds and ties, and the structures of care and protection. The book sheds light on the new roles of grandparents and new grandparents, and the empowerment and resilience initiatives, thereby providing a broad discussion of what the ageing society implies in psychosocial terms. These issues are addressed in an interdisciplinary way, but also in an approach that is also rare, comparing different realities between Europe and Latin America. The [basis of the] English translation of this book from its Spanish original manuscript was done with the help of artificial intelligence. A subsequent human revision of the content was done by the author.
Famous Problems of Geometry and How to Solve Them (Dover Books on Mathematics)
by Benjamin BoldIt took two millennia to prove the impossible; that is, to prove it is not possible to solve some famous Greek problems in the Greek way (using only straight edge and compasses). In the process of trying to square the circle, trisect the angle and duplicate the cube, other mathematical discoveries were made; for these seemingly trivial diversions occupied some of history's great mathematical minds. Why did Archimedes, Euclid, Newton, Fermat, Gauss, Descartes among so many devote themselves to these conundrums? This book brings readers actively into historical and modern procedures for working the problems, and into the new mathematics that had to be invented before they could be "solved."The quest for the circle in the square, the trisected angle, duplicated cube and other straight-edge-compass constructions may be conveniently divided into three periods: from the Greeks, to seventeenth-century calculus and analytic geometry, to nineteenth-century sophistication in irrational and transcendental numbers. Mathematics teacher Benjamin Bold devotes a chapter to each problem, with additional chapters on complex numbers and analytic criteria for constructability. The author guides amateur straight-edge puzzlists into these fascinating complexities with commentary and sets of problems after each chapter. Some knowledge of calculus will enable readers to follow the problems; full solutions are given at the end of the book.Students of mathematics and geometry, anyone who would like to challenge the Greeks at their own game and simultaneously delve into the development of modern mathematics, will appreciate this book. Find out how Gauss decided to make mathematics his life work upon waking one morning with a vision of a 17-sided polygon in his head; discover the crucial significance of eπi = -1, "one of the most amazing formulas in all of mathematics." These famous problems, clearly explicated and diagrammed, will amaze and edify curious students and math connoisseurs.
Fantastische Rätsel und wie Sie sie lösen können: Logik, Wahrscheinlichkeit, Geometrie, Spiele und mehr!
by Oliver RoederDie 49 verblüffendsten, beliebtesten und interessantesten Mathematikrätsel der Kolumne „The Riddler“ auf der Nachrichtenseite „FiveThirtyEight“ sind in diesem Buch für das kleine (oder größere) Rätselabenteuer zwischendurch gesammelt. Erforschen Sie dabei alltägliche Vorkommnisse mit Mathematik und Verstand:Wie Sie am besten Ihr Smartphone fallen lassenKönnen Sie den unsteten Prinzen finden?Die Quadratur des QuadratsVorsicht mit dem Martini-Glas!Können Sie die Alien-Invasion stoppen?Besetzt oder nicht besetzt – das ist hier die FrageUnd wenn Roboter Ihre Pizza schneiden?Werden Sie (ja Sie!) die Wahl entscheiden? Und vieles mehr! Die einfachsten Rätsel erfordern bloß einen Geistesblitz, während Sie für die schwierigsten schon ein gewisses Geschick in Analysis und Wahrscheinlichkeitstheorie benötigen. Die „Fantastischen Rätsel“ sind ein Muss für jeden Mathematik- oder Rätselliebhaber! "Ein modernes, intelligentes Rätselbuch, wie ich es noch nie zuvor gesehen habe, dessen mathematische und logische Herausforderungen Ihr Gehirn auf neue Art und Weise fordern werden" - Will Shortz, New York Times, NPR-PuzzlemasterDer HerausgeberOliver Roeder war Redakteur bei FiveThirtyEight und Herausgeber der mathematischen Kolumne „The Riddler“. Er hat in Wirtschaftswissenschaften mit Schwerpunkt Spieltheorie promoviert und war Nieman fellow an der Harvard University 2020. Er lebt in Brooklyn, New York.
Farb- und Formpsychologie
by Tobias C. BreinerDieses Werk ist eine umfassende und praxisrelevante Darstellung zur Farb- und Formpsychologie. Mit einer klaren Sprache und über 100 farbigen Abbildungen wird Ihnen die komplexe Thematik auf eine wissenschaftliche und anregende Art veranschaulicht.Über eine allgemeine Einführung in die Grundlagen des visuellen Systems hinaus werden Sie ebenfalls spezielles Wissen zu Assoziationen, Wirkungen und Anwendungen bestimmter Farben und Formen erwerben. Speziellen Wert legt der Autor dabei auf deren Einsatz im Game Design. Es wird zudem erstmals eine neue Farbstudie präsentiert, die zeigt, dass die Assoziationen zu Farben sich in einem in sich logischen dreidimensionalen System anordnen lassen. Die daraus gezogenen überraschenden Erkenntnisse liefern mögliche Antworten auf fundamentale Fragen der Philosophie. Das Buch ist daher nicht nur ein Muss für Wahrnehmungspsychologen und Designer, sondern eine Bereicherung für alle an dieser Thematik Interessierten.
Fascinating Mathematical People
by Philip J. Davis Gerald L. Alexanderson Donald J. AlbersFascinating Mathematical People is a collection of informal interviews and memoirs of sixteen prominent members of the mathematical community of the twentieth century, many still active. The candid portraits collected here demonstrate that while these men and women vary widely in terms of their backgrounds, life stories, and worldviews, they all share a deep and abiding sense of wonder about mathematics. Featured here--in their own words--are major research mathematicians whose cutting-edge discoveries have advanced the frontiers of the field, such as Lars Ahlfors, Mary Cartwright, Dusa McDuff, and Atle Selberg. Others are leading mathematicians who have also been highly influential as teachers and mentors, like Tom Apostol and Jean Taylor. Fern Hunt describes what it was like to be among the first black women to earn a PhD in mathematics. Harold Bacon made trips to Alcatraz to help a prisoner learn calculus. Thomas Banchoff, who first became interested in the fourth dimension while reading a Captain Marvel comic, relates his fascinating friendship with Salvador Dalí and their shared passion for art, mathematics, and the profound connection between the two. Other mathematical people found here are Leon Bankoff, who was also a Beverly Hills dentist; Arthur Benjamin, a part-time professional magician; and Joseph Gallian, a legendary mentor of future mathematicians, but also a world-renowned expert on the Beatles. This beautifully illustrated collection includes many photographs never before published, concise introductions by the editors to each person, and a foreword by Philip J. Davis.
Fashion Figures
by Melissa A. BorzaMissy Maker is a middle school girl who loves math and fashion. She sees math in everything she does. She tries to hide this from her friends, because she thinks it's too geeky. Missy hears that the school math club needs more members, but she's worried about what her friends will think if she joins, and she's already committed to joining the fashion club. After an epic internal struggle and with the support of her peers and her quirky, loving family, Missy finds that she can be both a Mathlete and a Fashionista. Missy figures out how to bring the two clubs together to help both groups win. In the process, she discovers that she can openly excel in math and science and still be popular with her peers. She also learns how her math and science skills can help her artistic endeavors. Gain an inside perspective on what it's like when you love math and science and happen to be a girl. Fashion Figures highlights the societal and internal pressures preteen and early-teen girls often face when they excel in these subjects, and it shows strategies for overcoming barriers to being themselves and doing what they love while still fitting in socially. What You'll Learn Girls can have a passion for STEM (science, technology, engineering and math) subjects and still be cool Girls can be great at math Math skills are important in non-STEM centered subject areas like fashion and art Math can be fun Who This Book Is For Pre-teen and early-teen girls (9-14 years old)
Fashion Math (Math 24/7 #10)
by Rae SimonsPeople who make clothes need to get their numbers right. From the length of fabric to the size of a pair of jeans, math plays an important role in the fashion industry. In Fashion Math, you'll learn some of the ways the math you learn in the classroom is important on the catwalk. You may even want to use that math to try your hand at making your own clothes!
Fashion, Faith, and Fantasy in the New Physics of the Universe
by Roger PenroseWhat can fashionable ideas, blind faith, or pure fantasy possibly have to do with the scientific quest to understand the universe? Surely, theoretical physicists are immune to mere trends, dogmatic beliefs, or flights of fancy? In fact, acclaimed physicist and bestselling author Roger Penrose argues that researchers working at the extreme frontiers of physics are just as susceptible to these forces as anyone else. In this provocative book, he argues that fashion, faith, and fantasy, while sometimes productive and even essential in physics, may be leading today's researchers astray in three of the field's most important areas--string theory, quantum mechanics, and cosmology.Arguing that string theory has veered away from physical reality by positing six extra hidden dimensions, Penrose cautions that the fashionable nature of a theory can cloud our judgment of its plausibility. In the case of quantum mechanics, its stunning success in explaining the atomic universe has led to an uncritical faith that it must also apply to reasonably massive objects, and Penrose responds by suggesting possible changes in quantum theory. Turning to cosmology, he argues that most of the current fantastical ideas about the origins of the universe cannot be true, but that an even wilder reality may lie behind them. Finally, Penrose describes how fashion, faith, and fantasy have ironically also shaped his own work, from twistor theory, a possible alternative to string theory that is beginning to acquire a fashionable status, to "conformal cyclic cosmology," an idea so fantastic that it could be called "conformal crazy cosmology."The result is an important critique of some of the most significant developments in physics today from one of its most eminent figures.